        The drawback of WENO-NS scheme is that all the three
sub-stencils \(S_{0}(j)\) , \(S_{1}(j)\)  and \(S_{2}(j)\)  may provide
unbalanced contribution to the evaluation point \(x_{j+\frac{1}{2}}\) 
because, the stencils \(S_{1}(j)\)  and \(S_{2}(j)\)  are symmetric with
respect to the point \(x_{j+\frac{1}{2}}\)  whereas \(S_{0}(j)\)  is not.
Therefore the interpolation process may be over-influenced to the
evaluation point from the left sub-stencils. For this, in [1]}
the authors improved the WENO-NS scheme by adjusting smoothness indicators
to the three sub-stencils by
\(\tilde{\beta _{0}}=\beta _{0},\,\,\tilde{\beta _{1}}=(1+\delta )\beta _{1},\,\,\tilde{\beta _{2}}=(1-\delta )\beta _{2}.\) 
